Stochastic Rules Research Articles

Introducing a new multi-particle collision method for the evolution of dense stellar systems

Context. Stellar systems are broadly divided into collisional and non-collisional categories. While the latter are large-N systems with long relaxation timescales and can be simulated disregarding two-body interactions, either computationally expensive direct N-body simulations or approximate schemes are required to properly model the former. Large globular clusters and nuclear star clusters, with relaxation timescales of the order of a Hubble time, are small enough to display some collisional behaviour and big enough to be impossible to simulate with direct N-body codes and current hardware. Aims. We aim to introduce a new method to simulate collisional stellar systems and validate it by comparison with direct N-body codes on small-N simulations. Methods. The Multi-Particle Collision for Dense Stellar Systems (MPCDSS) code is a new code for evolving stellar systems with the multi-particle collision method. Such a method amounts to a stochastic collision rule that makes it possible to conserve the exact energy and momentum over a cluster of particles experiencing the collision. The code complexity scales with N log N in the number of particles. Unlike Monte Carlo codes, MPCDSS can easily model asymmetric, non-homogeneous, unrelaxed, and rotating systems, while allowing us to follow the orbits of individual stars. Results. We evolved small (N = 3.2 × 104) star clusters with MPCDSS and with the direct-summation code NBODY6, finding a similar evolution of key indicators. We then simulated different initial conditions in the 104 − 106 star range. Conclusions. MPCDSS bridges the gap between small collisional systems that can be simulated with direct N-body codes and large non-collisional systems. In principle, MPCDSS allows us to simulate globular clusters such as Ω Centauri and M 54, and even nuclear star clusters, which is beyond the limits of current direct N-body codes in terms of the number of particles.

Rational Inattention Dynamics in Stochastic Games: Coordination and Conditioning

Decision-makers that choose information strategies instead of concrete actions elect stochastic choice rules that leave open the potential for errors, which can obfuscate the strategic interactions of players. This article establishes that dynamic, stochastic, games with rationally inattentive agents have Nash equilibria in which players coordinate their choice rules. When these choice rules are compliant with the predisposition of players towards particular actions, the Nash equilibria can be expressed in terms of dynamic logit rules. This result reduces finding Nash equilibria of this type to establishing a joint distribution of actions and states that accommodates the optimal behavior of all players. Logit rule Nash equilibria are used to study an example of strategic coordination, and an example of a zero-sum, strategic conflict game with sequential moves. The resulting equilibria of the second example involve strategies that exhibit conditioning characteristics and can be relevant for applications in principal-agent problems.

Worst-Case Stealthy Attacks on Stochastic Event-Based State Estimation

This article considers the worst-case stealthy attack strategies on stochastic event-based state estimation. Smart sensors equipped with local event-triggered Kalman filters are used to transmit innovations. Contrary to classic Kalman filters, the transmitted innovation screened by the stochastic decision rule does not follow a Gaussian distribution. A type of distribution called complete Gaussian crater is defined and analyzed, which is essential for designing stealthy attacks. The evolution of the estimation error covariance under attacks is obtained. Stealthy attacks that yield the greatest estimation errors under constraints on transmission rates and probability distributions are obtained and analyzed. The system performance degradation caused by different attacks is evaluated via simulations.

Coherent portfolio performance ratios

In Quantitative Finance 2016, Chen, Hu and Lin (CHL) claimed the following: ‘ … there is yet no coherent risk measure related to investment performance.’ (p. 682). Our paper suggests and analyzes four coherence axioms that portfolio performance ratios should satisfy. Our Portfolio Riskless Translation Invariance axiom must be satisfied to assure separation of the objective decision to optimize a portfolio’s risky composition from the subjective decision to optimize the weight of the portfolio's level of risk-free asset. Performance ratios with fixed thresholds other than the risk-free rate do not satisfy this axiom, allowing portfolio managers to affect an ex-ante performance ratio merely by changing the proportion of the risk-free asset in the portfolio rather than by improving the composition of the portfolio’s risky components. The magnitude of this potential drawback is examined using S&P-500 stock index data. Replacing the fixed threshold, T, with a threshold that equals γ times the portfolio’s risk premium plus (1-γ) times the risk-free rate, eliminates the above shortcoming for any selected γ. In addition, using performance ratios with threshold rather than fixed T, assures consistency of performance ratios of effective stochastic dominance and risk-free asset rules.

A Machine Learning Way to Classify Autism Spectrum Disorder

In recent times Autism Spectrum Disorder (ASD) is picking up its force quicker than at any other time. Distinguishing autism characteristics through screening tests is over the top expensive and tedious. Screening of the same is a challenging task, and classification must be conducted with great care. Machine Learning (ML) can perform great in the classification of this problem. Most researchers have utilized the ML strategy to characterize patients and typical controls, among which support vector machines (SVM) are broadly utilized. Even though several studies have been done utilizing various methods, these investigations didn't give any complete decision about anticipating autism qualities regarding distinctive age groups. Accordingly, this paper plans to locate the best technique for ASD classi-fication out of SVM, K-nearest neighbor (KNN), Random Forest (RF), Naïve Bayes (NB), Stochastic gradient descent (SGD), Adaptive boosting (AdaBoost), and CN2 Rule Induction using 4 ASD datasets taken from UCI ML repository. The classification accuracy (CA) we acquired after experimentation is as follows: in the case of the adult dataset SGD gives 99.7%, in the adolescent dataset RF gives 97.2%, in the child dataset SGD gives 99.6%, in the toddler dataset Ada-Boost gives 99.8%. Autism spectrum quotients (AQs) varied among several sce-narios for toddlers, adults, adolescents, and children that include positive predic-tive value for the scaling purpose. AQ questions referred to topics about attention to detail, attention switching, communication, imagination, and social skills.

Project Portfolio Selection Considering Uncertainty: Stochastic Dominance-Based Fuzzy Ranking

This paper proposes a method for project selection based on stochastic dominance (SD) and fuzzy theory. Using fuzzy theory and stochastic dominance, the method is tested using data from real-world projects. The findings show the importance of the proposed methodology improved existing methods in two ways: (1) This research alleviates the subjective bias in risk assessment in estimating the expected value hidden in the project portfolio (2) Adding the stochastic dominance rule to the fuzzy ranking process contributes to efficiency in project portfolio selection. The study contributes to the literature by exploring the combination of both fuzzy theory and stochastic dominance. For practitioner significance, managers can identify key uncertainty factors and estimate value in managing project portfolios.

Higher-Order Weak Schemes for the Heston Stochastic Volatility Model by Extrapolation

We consider a time-discrete scheme for the Heston stochastic volatility model, which employs the stochastic trapezoidal rule to discretize the logarithmic asset process, provided that the variance process is simulated exactly. We prove that, with respect to any polynomial function of the log-asset process, the weak error can be expanded to arbitrarily high powers of step size, which allows us to construct higher-order weak approximations by extrapolation. The result applies for the full parameter regime.

Alignment Percolation

The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \geqslant 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on $\mathbb {Z}^{d}$ with parameter p ∈ (0,1]. For each occupied site v, and for each of the 2d possible coordinate directions, declare the entire line segment from v to the next occupied site in the given direction to be either blue or not blue according to a given stochastic rule. In the ‘one-choice model’, each occupied site declares one of its 2d incident segments to be blue. In the ‘independent model’, the states of different line segments are independent.

Growth of tumours with stem cells: The effect of crowding and ageing of cells

Mathematical models for the growth of tumours in the presence of stem cells (CSCs) and differentiated tumour cells (CCs) are presented and discussed. The CSCs are assumed to be immortal and multipotent, i.e. capable of generating several possible lineages of CCs that may undergo ageing and apoptosis. Each CC is characterised by two indexes, related to the differentiation lineage and the class of age, respectively. Furthermore, the effect of crowding is taken into account, assuming that mitosis can be hindered by the presence of cells in the vicinity of the would-be mother cell. Two families of models are proposed. First, models based on cellular automata are considered, whose evolution is governed by stochastic rules. Then, by averaging over the cells with the same pair of indexes, we obtain a deterministic model that consists of a system of Ordinary Differential Equations (ODEs) whose unknown functions are the fractions of the cells in each lineage and the class of age. The system presents a basic novelty with respect to the other compartmental models proposed in the literature as it cannot be solved hierarchically because of the presence of the crowding effect. Numerical simulations based on the two families of models give the same qualitative results and, in particular, they evidentiate the occurrence of the tumour paradox: an increased mortality of the CCs may induce a faster growth of the tumour. A final section of the paper is devoted to the case in which the age distribution of the CCs is continuous and not discrete. In this case, an interesting mathematical problem is obtained that consists of one ODE for the fraction of CSCs and m first-order Partial Differential Equations (PDEs); one for each lineage of CCs.

On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling

During developmental angiogenesis, endothelial cells respond to shear stress by migrating and remodelling the initially hyperbranched plexus, removing certain vessels whilst maintaining others. In this study, we argue that the key regulator of vessel preservation is cell decision behaviour at bifurcations. At flow-convergent bifurcations where migration paths diverge, cells must finely tune migration along both possible paths if the bifurcation is to persist. Experiments have demonstrated that disrupting the cells’ ability to sense shear or the junction forces transmitted between cells impacts the preservation of bifurcations during the remodelling process. However, how these migratory cues integrate during cell decision making remains poorly understood. Therefore, we present the first agent-based model of endothelial cell flow-mediated migration suitable for interrogating the mechanisms behind bifurcation stability. The model simulates flow in a bifurcated vessel network composed of agents representing endothelial cells arranged into a lumen which migrate against flow. Upon approaching a bifurcation where more than one migration path exists, agents refer to a stochastic bifurcation rule which models the decision cells make as a combination of flow-based and collective-based migratory cues. With this rule, cells favour branches with relatively larger shear stress or cell number. We found that cells must integrate both cues nearly equally to maximise bifurcation stability. In simulations with stable bifurcations, we found competitive oscillations between flow and collective cues, and simulations that lost the bifurcation were unable to maintain these oscillations. The competition between these two cues is haemodynamic in origin, and demonstrates that a natural defence against bifurcation loss during remodelling exists: as vessel lumens narrow due to cell efflux, resistance to flow and shear stress increases, attracting new cells to enter and rescue the vessel from regression. Our work provides theoretical insight into the role of junction force transmission has in stabilising vasculature during remodelling and as an emergent mechanism to avoid functional shunting.

A New Mathematical Model for Controlling Tumor Growth Based on Microenvironment Acidity and Oxygen Concentration.

Hypoxia and the pH level of the tumor microenvironment have a great impact on the treatment of tumors. Here, the tumor growth is controlled by regulating the oxygen concentration and the acidity of the tumor microenvironment by introducing a two-dimensional multiscale cellular automata model of avascular tumor growth. The spatiotemporal evolution of tumor growth and metabolic variations is modeled based on biological assumptions, physical structure, states of cells, and transition rules. Each cell is allocated to one of the following states: proliferating cancer, nonproliferating cancer, necrotic, and normal cells. According to the response of the microenvironmental conditions, each cell consumes/produces metabolic factors and updates its state based on some stochastic rules. The input parameters are compatible with cancer biology using experimental data. The effect of neighborhoods during mitosis and simulating spatial heterogeneity is studied by considering multicellular layer structure of tumor. A simple Darwinist mutation is considered by introducing a critical parameter (Nmm) that affects division probability of the proliferative tumor cells based on the microenvironmental conditions and cancer hallmarks. The results show that Nmm regulation has a significant influence on the dynamics of tumor growth, the growth fraction, necrotic fraction, and the concentration levels of the metabolic factors. The model not only is able to simulate the in vivo tumor growth quantitatively and qualitatively but also can simulate the concentration of metabolic factors, oxygen, and acidity graphically. The results show the spatial heterogeneity effects on the proliferation of cancer cells and the rest of the system. By increasing Nmm, tumor shrinkage and significant increasing in the oxygen concentration and the pH value of the tumor microenvironment are observed. The results demonstrate the model's ability, providing an essential tool for simulating different tumor evolution scenarios of a patient and reliable prediction of spatiotemporal progression of tumors for utilizing in personalized therapy.

Noise-Boosted Backpropagation Learning of Feedforward Threshold Neural Networks for Function Approximation

Aiming to ensure the feasibility of the backpropagation training of feedforward threshold neural networks, each hidden unit layer is designed to be composed of a sufficiently large number of hard-limiting activation functions that are excited by mutually independent external noise components and the weighted inputs simultaneously. The application of noise to nondifferentiable activation functions enables a proper definition of the gradients, and the injected noise is treated as a network parameter that can be adaptively updated by a stochastic gradient descent learning rule. This noise-boosted backpropagation learning process is found to converge to a nonzero optimized level of noise, indicating that the injected noise is beneficial both for the learning and for the ensuing retrieval phase. For minimizing the total error energy of the function approximation in the designed threshold neural network, the proposed noise-boosted backpropagation learning method is proven to be better than directly injecting noise into network inputs or weight coefficients. The Lipschitz continuous property of the noise-smoothed activation function in the hidden unit layer is demonstrated to guarantee the local convergence of the learning process. Beyond the Gaussian injected noise, the optimal noise type is also numerically solved for training the designed threshold neural network. Test experiments for approximating nonlinear functions and real-world datasets verify the feasibility of this noise-boosted backpropagation algorithm in the threshold neural network. These results not only extend the analysis of the beneficial effects of noise similar to stochastic resonance and exploited here to the universal approximation capabilities of threshold neural networks, but also allow backpropagation training of neural networks with a much wider family of nondifferentiable activation functions.

The Dynamics of the House Price-to-Income Ratio: Theory and Evidence

The house price-to-income ratio (PIR) is widely used as an affordability indicator. This paper complements the cross-sectionally focused literature by proposing a tractable model for the PIR dynamics. Our model predicts that the PIR is very persistent and is correlated to the lagged aggregate output. Cross-country analysis confirms this prediction and provides evidence for a long-term, positive and significant relationship between PIR and aggregate production. Our results hint at the construction of an early warning system for housing market mispricing. Our tractable formulation of a stochastic money growth rule may carry independent research interest.

Space-velocity thermostatted kinetic theory model of tumor growth.

The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during favorable interactions. The cell activity fluctuations are controlled by a thermostat. The direction of cell velocity is changed according to stochastic rules mimicking a dense fluid. We develop a kinetic Monte Carlo algorithm inspired from the direct simulation Monte Carlo (DSMC) method initially used for dilute gases. The simulations generate stochastic trajectories sampling the kinetic equations for the distributions of the different cell types. The evolution of an initially localized tumor is analyzed. Qualitatively different behaviors are observed as the field regulating activity fluctuations decreases. For high field values, i.e. efficient thermalization, cancer is controlled. For small field values, cancer rapidly and monotonously escapes from immunosurveillance. For the critical field value separating these two domains, the 3E's of immunotherapy are reproduced, with an apparent initial elimination of cancer, a long quasi-equilibrium period followed by large fluctuations, and the final escape of cancer, even for a favored production of immune system cells. For field values slightly smaller than the critical value, more regular oscillations of the number of immune system cells are spontaneously observed in agreement with clinical observations. The antagonistic effects that the stimulation of the immune system may have on oncogenesis are reproduced in the model by activity-weighted rate constants for the autocatalytic productions of immune system cells and cancer cells. Local favorable conditions for the launching of the oscillations are met in the fluctuating inhomogeneous system, able to generate a small cluster of immune system cells with larger activities than those of the surrounding cancer cells.

Estimating the Critical Parameter in Almost Stochastic Dominance from Insurance Deductibles

Knowing how small a violation of stochastic dominance rules would be accepted by most individuals is a prerequisite to applying almost stochastic dominance criteria. Unlike previous laboratory-experimental studies, this paper estimates an acceptable violation of stochastic dominance rules with 939,690 real world data observations on a choice of deductibles in automobile theft insurance. We find that, for all policyholders in the sample who optimally chose a low deductible, the upper bound estimate of the acceptable violation ratio is 0.0014, which is close to zero. On the other hand, considering that most decision makers, such as 99% (95%) of the policyholders in the sample, optimally chose the low deductible, the upper bound estimate of the acceptable violation ratio is 0.0405 (0.0732). Our results provide reference values for the acceptable violation ratio for applying almost stochastic dominance rules. This paper was accepted by Manel Baucells, decision analysis.

Stochastic simulation of phytoplankton biomass using eighteen years of daily data - predictability of phytoplankton growth in a large, shallow lake

During the past decades, on-line monitoring of freshwater lakes has developed rapidly. To use high frequency time-series in lake management, novel models are needed that are simple and provide insight into the complexity of phytoplankton dynamics. Chlorophyll a (Chl), a proxy for phytoplankton biomass and environmental drivers were monitored on-line in large, shallow Lake Balaton during the vegetation periods between 2001 and 2018. Growth and non-growth (G and non-G) states of algae were deduced from daily change in Chl. Random forests (RF) were used to find stochastic response rules of phytoplankton to growth-supporting environmental habitat templates. The stochastic G/non-G state was translated into long-term daily biomass dynamics by a deterministic biomass model to assess uncertainty and to distinguish between inevitable and unpredictable blooms. A biomass peak was qualified as inevitable or unpredictable if the lower 95% confidence limit of simulations exceeded or remained at the baseline Chl level, respectively. Compared to a stochastic null model based on monthly Markovian transition probabilities, RF-based models captured wax and wane of biomass realistically. Timing of peaks could be better simulated than their magnitude, likely because habitat templates were primarily determined by light whereas peak sizes might depend on unmeasured processes, such as phosphorus availability. In general, algal growth was favored by wind-induced sediment resuspension that decreased light availability but simultaneously enhanced the P supply. Seasonal temperature and an integral of departures from the “normal” seasonal temperature over 2 to 3 generations were important drivers of phytoplankton growth, whereas short-term (diel and day to day) changes in water temperature appeared to be irrelevant. Four types of years could be distinguished during the study period with respect to algal growth conditions. The present modeling approach can reasonably be used even in highly variable aquatic environments when 3 to 4 years of daily data are available.

Stochastic and Strategy-Proof Auctions for Statistical Inferences

We study a stochastic auction in a multi-items and unit-demand setting where bidders have one-dimensional type spaces. In a usual Pareto-efficient auction such as the VCG auction, items are allocated deterministically to bidders depending on their bids. However, even if an auctioneer implements a deterministic auction repeatedly, data that the auctioneer and bidders can get from the auction would be limited because the bidder with the highest bid gets the best item, the bidder with second highest bid gets the second best item, and so on surely. Then, for example, the auctioneer cannot infer what happens if the best item was allocated to the other bidder. We consider a stochastic auction which allocates items stochastically to bidders according to their bids in order to get rich data. We introduce a stochastic auction rule that is strategy-proof and individual rational. Moreover, we show that our stochastic auction can be used to get rich data, and yields relatively high revenue compared to the VCG auction in a computer experiment.

Deterministic and Stochastic Rules of Branching Govern Dendrite Morphogenesis of Sensory Neurons

Dendrite morphology is necessary for the correct integration of inputs that neurons receive. The branching mechanisms allowing neurons to acquire their type-specific morphology remain unclear. Classically, axon and dendrite patterns were shown to be guided by molecules, providing deterministic cues. However, the extent to which deterministic and stochastic mechanisms, based upon purely statistical bias, contribute to the emergence of dendrite shape is largely unknown. We address this issue using the Drosophila class I vpda multi-dendritic neurons. Detailed quantitative analysis of vpda dendrite morphogenesis indicates that the primary branch grows very robustly in a fixed direction, though secondary branch numbers and lengths showed fluctuations characteristic of stochastic systems. Live-tracking dendrites and computational modeling revealed how neuron shape emerges from few local statistical parameters of branch dynamics. We report key opposing aspects of how tree architecture feedbacks on the local probability of branch shrinkage. Child branches promote stabilization of parent branches, although self-repulsion promotes shrinkage. Finally, we show that self-repulsion, mediated by the adhesion molecule Dscam1, indirectly patterns the growth of secondary branches by spatially restricting their direction of stable growth perpendicular to the primary branch. Thus, the stochastic nature of secondary branch dynamics and the existence of geometric feedback emphasize the importance of self-organization in neuronal dendrite morphogenesis.

Mining stochastic cellular automata to solve density classification task in two dimensions

Density Classification Task (DCT) is a well-known problem that researchers have been tackling for more than two decades, where the main goal is to build a cellular automaton whose local rule gives rise to emergent global coordination. We describe the methods used to identify new cellular automata that solve this problem. The design of our cellular automata was carried out by a parallel genetic algorithm, specifically instantiated for this task. Our approach identifies both the neighborhood and its stochastic rule using a dataset of initial configurations that covers in a predefined and balanced way the full range of densities in DCT. We compare our results with some models currently available in the field. In some cases, our models show better performance than the best solution reported in the literature, with efficacy of 0.842 for datasets with uniform distribution around the critical density. The best-known cellular automaton achieves 0.832 in the same datasets. Tests are carried out in datasets of diverse lattice sizes and sampling conditions; we focused the analysis on the performance of our model around critical densities. Finally, by a statistical non-parametric test, we demonstrate that there are no significant differences between our identified cellular automata and the best-known model.

A revelation principle for obviously strategy-proof implementation

We consider probabilistic versions of obviously strategy-proof implementation (Li, 2017) for stochastic rules, and provide an algorithm involving several ideas from the literature (Ashlagi and Gonczarowski, 2018; Pycia and Troyan, 2016; Bade and Gonczarowski, 2017) that converts any such implementation into a randomized round table implementation, where the administrator randomly selects a game form in which agents take turns making public announcements about their private information (Theorem 1). We provide an analogous algorithm for sure implementation of deterministic rules (Theorem 2); this builds on related results from the literature by (i) relaxing all recall requirements, (ii) allowing randomization by the agents, and (iii) allowing all game trees for which choices determine plays (Alós-Ferrer and Ritzberger, 2016). We discuss a variety of implications and related topics.